Colimits of monoids
Abstract
If C is a cocomplete monoidal category in which tensoring from both sides preserves coequalizers, then the category of monoids over C is cocomplete. The same holds if C has regular factorizations and tensoring only preserves regular epimorphisms. As an application a lifting theorem for an adjunction with a monoidal right adjoint to an adjunction between the respective categories of monoids is proved.
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